Being absolutely clueless, I can't help but think that it looks somewhat like a fragment of a belemnite rostrum (althogh flattened - but why care about details?). The size of it might indicate something like Acroteuthis, perhaps?

Below is a picture of the best Pinna that I have found on the Holderness, you can find them quite easily just north of the Peak fault at Ravenscar in Robin Hoods Bay, but they are not very collectable because they tend to crumble and usually donot come out whole.